Experimental study on interfacial area transport in vertical upward bubbly two-phase flow in an annulus

In relation to the development of the interfacial area transport equation, axial developments of local void fraction, interfacial area concentration, and interfacial velocity of vertical upward bubbly flows in an annulus with the hydraulic equivalent diameter of 19.1 mm were measured by the double-sensor conductivity probe. A total of 20 data were acquired consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. The obtained data will be used for the development of reliable constitutive relations, which reflect the true transfer mechanisms in subcooled boiling flow systems.     

Axial developments of interfacial area and void concentration profiles in subcooled boiling flow of water

Axial developments of the local void fraction, interfacial area concentration and bubble Sauter mean diameter were measured in subcooled boiling flow of water in a vertical internally heated annulus using the double-sensor conductivity probe technique. Measurements were performed under varying conditions of heat flux, inlet liquid velocity and inlet liquid temperature. A total of 10 data sets were acquired. Based on these measurements with the previous data obtained in the present test loop, the influence of flow condition on the profiles of local two-phase flow parameters was discussed. The measured average void fraction and interfacial area concentration were compared with the predictions by existing correlations for drift-flux parameters and interfacial area concentration. Also, the recently proposed bubble layer thickness model in subcooled boiling was evaluated for the measurement data.     

Flow structure of subcooled boiling flow in an internally heated annulus

Local measurements of flow parameters were performed for vertical upward subcooled boiling flows in an internally heated annulus. The annulus channel consisted of an inner heater rod with a diameter of 19.1 mm and an outer round pipe with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. The double-sensor conductivity probe method was used for measuring local void fraction, interfacial area concentration, and interfacial velocity. A total of 11 data were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s and two inlet liquid temperatures, 95.0 and 98.0 °C. The constitutive equations for distribution parameter and drift velocity in the drift-flux model, and the semi-theoretical correlation for Sauter mean diameter, namely, interfacial area concentration, which were proposed previously, were validated by local flow parameters obtained in the experiment.     

Axial development of interfacial structure of vertical downward bubbly flow

Accurate prediction of the interfacial area concentration is essential to successful development of the interfacial transfer terms in the two-fluid model. Mechanistic modeling of the interfacial area concentration entirely relies on accurate local flow measurements over extensive flow conditions and channel geometries. From this point of view, accurate measurements of flow parameters such as void fraction, interfacial area concentration, and interfacial velocity were performed by a multi-sensor probe at three axial locations as well as seven radial locations in vertical downward bubbly flows using a 25.4 mm-diameter pipe. In the experiment, the superficial liquid velocity and the void fraction ranged from −1.25 to −3.11 m/s and from 1.61% to 21.0%, respectively.     

Local flow measurements of vertical upward bubbly flow in an annulus

Local measurements of flow parameters were performed for vertical upward bubbly flows in an annulus. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. Double-sensor conductivity probe was used for measuring void fraction, interfacial area concentration, and interfacial velocity, and laser Doppler anemometer was utilized for measuring liquid velocity and turbulence intensity. A total of 20 data sets for void fraction, interfacial area concentration, and interfacial velocity were acquired consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. A total of eight data sets for liquid velocity and turbulence intensity were acquired consisting of two void fractions, about 0.050, and 0.10, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s. The constitutive equations for distribution parameter and drift velocity in the drift-flux model, and the semi-theoretical correlation for Sauter mean diameter namely interfacial area concentration, which were proposed previously, were validated by local flow parameters obtained in the experiment using the annulus.     

Two-phase phase distribution in a vertical large diameter pipe

In view of the practical importance of the application of two-phase flow in a large diameter pipe to various fields of engineering, the characteristics and phase distribution patterns of two-phase flow in a vertical large diameter pipe have been experimentally and theoretically studied for various flow conditions. The local measurements for the interfacial parameters (void fraction, Sauter mean diameter and pressure loss) in a vertical upward air-water two-phase flow in a pipe with 0.2 m in inner diameter and 24 m in height have been performed by using the optical probes and differential pressure transducers. The two-phase flow characteristics have been analyzed with experimental data, which shows that the phase distribution patterns in the vertical large diameter pipe can be divided into two basic patterns, namely, wall peak and core peak. With the application of the concept of skewness, the two-phase distribution patterns have been quantitatively distinguished by establishing a phase distribution pattern transition criterion. An empirical relation for the phase distribution transition from wall peak to core peak was fitted by using the phase distribution pattern transition criterion and the present experimental data and verified by other researchers’ experimental data. This study also showed that there existed the flow plugging phenomena in the low region of the test section at high superficial gas velocity conditions in the vertical large diameter pipe.     

Interfacial area transport of vertical upward bubbly two-phase flow in an annulus

In relation to the development of the interfacial area transport equation in a subcooled boiling flow, the one-dimensional interfacial area transport equation was evaluated by the data taken in the hydrodynamic separate effect tests without phase change, or an adiabatic air-water bubbly flow in a vertical annulus. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. Twenty data sets consisting of five void fractions, about 0.050, 0.10, 0.15, 0.20, and 0.25, and four superficial liquid velocities, 0.272, 0.516, 1.03, and 2.08 m/s were used for the evaluation of the one-dimensional interfacial area transport equation. The one-dimensional interfacial area transport equation agreed with the data with an average relative deviation of ±8.96%. Sensitivity analysis was also performed to investigate the effect of the initial bubble size on the interfacial area transport. It was shown that the dominant mechanism of the interfacial area transport was strongly dependent on the initial bubble size.     

A BUBBLE MECHANISTIC MODEL FOR SUBCOOLED BOILING FLOW PREDICTIONS

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUSIG (Multiple-Size-Group) model implemented in CFX4.4 is extended to account for the wall nucleation and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter diameter, interfacial area concentration, bubble population density, and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Good agreement is achieved with the local radial void fraction, bubble Sauter diameter, interfacial area concentration, bubble population density, and liquid velocity profiles against measurements. However, further improvement is needed for the accurate prediction of the vapor velocity using the present bubble mechanistic model. A proposal to include an algebraic slip model to account for bubble separation in the MUSIG boiling model is presented.     

Interfacial area concentration in annular two-phase flow

Accurate prediction of the interfacial area concentration is essential to successful development of the interfacial transfer terms in the two-fluid model. The interfacial area concentration in annular flow and annular-mist flow is especially relevant to the transition process to the liquid film dryout, which might lead to fatal problem in the safety and efficient operation of boiling heat transfer system. However, very few experimental and theoretical studies focusing on the interfacial area concentration in annular flow region have been conducted. From this point of view, measurements of annular flow parameters such as one-dimensional interfacial area concentration of liquid film and local interfacial area concentration profile of liquid film were performed by a laser focus displacement meter at 21 axial locations in vertical upward annular two-phase flow using a 3-m-long and 11-mm-diameter pipe. The axial distances from the inlet (z) normalized by the pipe diameter (D) varied over z/D = 50–250. Data were collected for preset gas and liquid flow conditions and for Reynolds numbers ranging from 31,800 to 98,300 for the gas phase and 1050 to 9430 for the liquid phase. Axial development of the one-dimensional interfacial area concentration and the non-dimensional local interfacial area concentration profile of liquid film were examined with the data obtained in the experiment. Total interfacial area concentration including liquid film and droplets was also discussed with help of the existing drift-flux model, entrainment correlation, and droplet size correlation.     

PREDICTION AND MEASUREMENT OF LOCAL TWO-PHASE FLOW PARAMETERS IN A BOILING FLOW CHANNEL

A two-fluid model to predict subcooled boiling flow at low pressure is presented. Although considerable success has been achieved in good axial predictions, this study focuses on the capability of the model to predict local two-phase flow parameters within an annulus channel. Comparison of model predictions is made against local measurements carried out by our Korean collaborators. Although reasonable agreement of local profiles of the void fraction, interfacial area concentration, and bubble frequency were achieved, significant weakness of the model was evidenced in the prediction of the mean Sauter diameter, liquid, and vapor velocities. The formulation of a transport equation to account for the dynamically changing interfacial area concentration is proposed. Further modeling work is in progress to incorporate the bubble coalescence behaviour seen during experiments into the transport equation.     

Effect of Void Fraction and Two-Phase Dynamic Viscosity Models on Prediction of Hydrostatic and Frictional Pressure Drop in Vertical Upward Gas–Liquid Two-Phase Flow

In gas–liquid two-phase flow, the prediction of two-phase density and hence the hydrostatic pressure drop relies on the void fraction and is sensitive to the error in prediction of void fraction. The objectives of this study are to analyze dependence of two-phase density on void fraction and to examine slip ratio and drift flux model-based correlations for their performance in prediction of void fraction and two-phase densities for the two extremes of two-phase flow conditions, that is, bubbly and annular flow or, alternatively, the low and high region of the void fraction. It is shown that the drift flux model-based correlations perform better than the slip ratio model-based correlations in prediction of void fraction and hence the two-phase mixture density. Another objective of this study is to verify performance of different two-phase dynamic viscosity models in prediction of two-phase frictional pressure drop. Fourteen two-phase dynamic viscosity models are assessed for their performance against 616 data points consisting of 10 different pipe diameters in annular flow regime. It is found that none of these two-phase dynamic viscosity models are able to predict the frictional pressure drop in annular flow regime for a range of pipe diameters. The correlations that are successful for small pipe diameters fail for large pipe diameters and vice versa.     

Acoustic Wave Prediction in Flowing Steam-Water Two-Phase Mixture

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Mechanistic study for the interfacial area transport phenomena in an air/water flow condition by using fine-size bubble group model

A set of number density transport equations based on the bubble size are used to predict the void fraction and the interfacial area concentration in an air/water flow conditions. As the closure relations for the number density transport equations, a coalescence due to random collisions and a breakup due to an impact of the turbulent eddies are modified based on previous studies. The bubble expansion term due to a pressure reduction and a coalescence due to a wake entrainment are modeled for the number density transport equation. In order to predict the local experimental data, a computational fluid dynamic (CFD) code coupling the two-fluid model and number density transport equations are developed in this study. As for the results of the numerical analysis, the developed model predicts well the void fraction and interfacial area concentration although some deviations between the prediction and the experiment are shown for the high void fraction conditions.     

Validation of void fraction models and correlations using a flow pattern transition mechanism model in relation to the identification of annular vertical downflow in-tube condensation of R134a

This paper reports the experimental investigation of a model for predicting flow pattern transitions and for the validation of void fraction models and correlations proposed in the authors' previous publications and for the identification of flow regimes in data corresponding to annular flow downward condensation of R134a in a vertical smooth copper tube having an inner diameter of 8.1 mm and a length of 500 mm. R134a and water are used as working fluids on the tube side and annular side, respectively, of a double tube heat exchanger. Condensation experiments are done at mass fluxes of 260 and 515 kg m^− 2 s^− 1 in the high mass flux region of R134a. The condensing temperatures are between 40 and 50 °C; heat fluxes are between 10.16 and 66.61 kW m^− 2. A mathematical model proposed by Soliman based on the models of Kosky and Lockhart–Martinelli is used to determine the condensation film thickness of R134a. Comparative void fraction values are determined indirectly using the measured data under laminar and turbulent flow conditions together with various void fraction models and correlations reported in the literature. There is good agreement between the void fraction results obtained from the theoretical model and those obtained from the void fraction models of Soliman, Chisholm and Armand, Turner and Wallis, Smith, Spedding and Spence previously proposed in the authors' publications and tested against their experimental database. Various well-known flow regime correlations from the literature are investigated to identify the flow regime occurring in the test tube, the correlations of Taitel and Dukler, Dobson, Akbar et al., Breber et al., Cavallini et al., and Sardesai et al. can provide accurate estimates of the annular flow conditions in spite of their different working conditions.     

Distribution parameter and drift velocity of drift-flux model in bubbly flow

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the distribution parameter and the drift velocity have been studied for bubbly flow regime. The constitutive equation that specifies the distribution parameter in the bubbly flow has been derived by taking into account the effect of the bubble size on the phase distribution, since the bubble size would govern the distribution of the void fraction. A comparison of the newly developed model with various fully developed bubbly flow data over a wide range of flow parameters shows a satisfactory agreement. The constitutive equation for the drift velocity developed by Ishii has been reevaluated by the drift velocity calculated by local flow parameters such as void fraction, gas velocity and liquid velocity measured under steady fully developed bubbly flow conditions. It has been confirmed that the newly developed model of the distribution parameter and the drift velocity correlation developed by Ishii can also be applicable to developing bubbly flows.     

Characteristics of Two-Phase Flows in a Rectangular Microchannel with a T-Junction Type Gas-Liquid Mixer

In this study, gas–liquid two-phase flows in a horizontal rectangular microchannel have been investigated. The rectangular microchannel has a hydraulic diameter of 0.235 mm, and a width and depth of 0.24 mm and 0.23 mm, respectively. A T-junction-type gas–liquid mixer was used to introduce gas and liquid in the channel. In order to know the effects of liquid properties, distilled water, ethanol, and HFE7200 were used as the test liquids, with nitrogen gas was used as the test gas. The flow pattern, the bubble length, the liquid slug length, and the bubble velocity in two-phase flow were measured with a high-speed video camera, and the void fraction was determined from the bubble velocity data and the superficial gas velocity data. In addition, the pressure drop was also measured with a calibrated differential pressure transducer. The bubble length data were compared with the calculation by the scaling law proposed by Garstecki et al. [7]. The bubble velocity data and/or the void fraction data were well correlated with the well-known drift flux model [12] with a new distribution parameter correlation developed in this study. The frictional pressure drop data were also well correlated with the Lockhart-Martinelli method with a correlation of the two-phase friction multiplier.     

Experimental identification of the phenomenon triggering the net vapor generation in upward subcooled flow boiling of water at low pressure

Observation of the bubble behavior was made using a high-speed camera to investigate the mechanisms to cause the net vapor generation in subcooled flow boiling. In the experiments, water was used as the test fluid, the flow direction was vertical upward, and the pressure was kept close to the atmospheric pressure. At high liquid subcooling close to the condition of the onset of nucleate boiling, all the bubbles were lifted off the heated surface immediately after the nucleation to disappear quickly in the subcooled bulk liquid due to condensation. It was found that the void fraction did not increase significantly unless the liquid subcooling became low enough for some bubbles to be reattached to the heated surface after the lift-off. When the reattachment took place, the bubble lifetime was substantially elongated since the bubbles slid up the vertical heated surface for a long distance after the reattachment. The reattachment therefore contributed to an increase in the void fraction. It was concluded that in the experimental conditions tested in this work, the bubble reattachment to the heated surface was a key phenomenon to cause the sharp increase of the void fraction at the point of net vapor generation.     

Gas–Liquid Two-Phase Flow Evolution in a Long Microchannel

A pair of optical void sensors and a high-speed video camera were used to investigate the evolution of adiabatic gas–liquid two-phase flow in a long microchannel. Experiments were conducted with a 1676-mm-long, circular microchannel with an inner diameter of 100 μm. Two-phase flow patterns, void fraction, and velocities of gas plug/slug and liquid slugs were measured at different axial locations between the gas–liquid mixer and microchannel exit. The pressure decreased linearly in the first half of the microchannel, and more rapidly and nonlinearly in the second half of the test section. As a result, the flow accelerated significantly in the second half of the microchannel such that the void fraction and liquid slug velocity increased nonlinearly. The measured mean void fraction and mean velocity of liquid slugs also agreed well with the homogeneous flow model predictions when the liquid flow rate was constant and the mass velocity of the gas was low.     

Two-phase flow in converging and diverging microchannels with CO2 bubbles produced by chemical reactions

The present study investigates experimentally the evolution of two-phase flow pattern and pressure drop in the converging and diverging, silicon-based microchannels with mean hydraulic diameter of 128 μm and CO₂ bubbles produced by chemical reactions of sulfuric acid (H₂SO₄) and sodium bicarbonate (NaHCO₃). Three different concentrations of 0.2, 0.5 and 0.8 mol/L of each reactant at the inlet before mixing and 10 different flow rates from 1.60 × 10⁻⁹ m³/s to 16.0 × 10⁻⁹ m³/s are studied. Flow visualization is made possible by using a high-speed digital camera. It is found that the present design of the microchannel, with the inlet chamber, results in much more intensive chemical reactions in the diverging microchannel than that in the converging one. The void fractions at the entrance and exit regions and pressure drop through the channel are also measured. The results reveals that the presence of small void fraction, <0.1, at the inlet may promote CO₂ generation in the microchannel, irrespective of the channel is converging or diverging, indicating the agitation effects of bubbly flow in the microchannel. The increase of inlet concentration of reactants does not increase the pressure drop in the converging microchannel significantly, while the inlet concentration presents significant but mild effects on the pressure drop in the diverging microchannel. The two-phase frictional multiplier may be positively correlated with the mean void fraction in the channel linearly, and the data agree well with predictions from the correlations in the literature.